Redistribution, Fiscal Competition, and the
Politics of Economic Integration∗
Anke S. Kessler†
Christoph Lülfesmann
Gordon M. Myers
University of Bonn
University of Bonn
Simon Fraser University
this version: December 2001
Abstract
The paper examines the consequences of the economic integration of factor
markets in a model with two countries that redistribute income among their residents. The social benefits in each country are financed by a source based tax
on capital which is democratically chosen by its inhabitants. If either capital or
labour is internationally mobile, the countries engage in fiscal competition and
the partial integration of capital or labour markets is detrimental to the countries’ redistributive ability. A move from partial to full integration, however, may
alleviate rather than intensify fiscal competition, particularly, if the two countries
face sufficiently similar economic and political conditions. In such a situation,
for example, tax competition for mobile capital is softened as the labour market
becomes more integrated and even vanishes if both factors are fully mobile. As a
result, there is more redistribution in equilibrium and a majority of the population
∗
This paper has benefitted from comments by Jan Brueckner, Ig Horstmann, Dave Wildasin, and
various participants of seminars at Bonn, Heidelberg, Konstanz, Mannheim, the 2001 Verein für Socialpolitik meeting, the 2001 ASSA meetings, and the 2000 World Congress of the Econometric Society.
We are also indebted to two anonymous referees and the Editor Mark Armstrong who provided valuable
comments on earlier versions. A first draft of this paper was written when Gordon Myers visited the
Universities of Bonn and Essex in 1997/1998. He wishes to thank both for their hospitality. Anke
Kessler (corresponding author) and Christoph Lülfesmann wish to thank the Haas School of Business
at UC Berkeley and Simon Fraser University for their hospitality. Financial support by the German
Academic Exchange Service (’Hochschulsonderprogramm III’), the Deutsche Forschungsgemeinschaft
through SFB 303 at the University of Bonn, SFHCR and SSHRC is gratefully acknowledged. Remaining
errors are our own.
†
Corresponding Author. University of Bonn and CEPR. Address: Department of Economics, University of Bonn, Adenauerallee 24-42, 53113 Bonn, Germany, e-mail: kessler@wiwi.uni-bonn.de, phone:
+49-228-739246, fax: +49-228-739221.
in each country is strictly better off.
JEL Classification: D78, H23, H 77
Keywords: Tax Competition, Fiscal Federalism, Factor Market Integration, Welfare Migration
2
1. INTRODUCTION
In the past decades, the world economy has experienced a movement toward ever increasing economic integration. As new technologies have reduced migration and communication costs and institutional or political barriers to mobility have been removed, the
mobility of goods, services, capital and – to a lesser extent – labour, has grown rapidly.
While the efficiency gains from common markets are largely undisputed, economists and
practitioners alike have expressed their concern with regard to the implications of this
development for the ability and the willingness of countries to provide public services
and to pursue redistributive policies at the national level.
The competition for mobile capital, in particular, is considered by some as one
of the greatest dangers to the survival of the welfare state. As a CEPR report on
subsidiarity within Europe (1993, p. 89) concludes: “the erosion of capital income as
part of the general tax base clearly has important implications for income and wealth
distribution”. This view is supported both by empirical evidence and by the theoretical
literature on tax competition. On average, corporate tax rates fell by 6 points and top
tax rates on interest income by 13 points for OECD countries during the 1980s.1 Formal
models [Gordon (1983), Zodrow and Mieszkowski (1986), Wilson (1987)] show that
competition for mobile capital results in suboptimally low levels of taxation and public
good provision. As a consequence, countries could gain from centrally coordinating their
national tax policies.
Although less pronounced, the integration of labour markets has also been seen as
undermining the ability of governments to redistribute income among their citizens.2
Sinn (2000, p. 6), for instance, predicts that “in the competition for the lowest possible
1
See Edwards and Keen (1996), who also present evidence from Scandinavian countries. In the early
1990’s, first Sweden, then Norway, then Finland reformed their capital income tax system, resulting in
reduced flat rates in the range of 30% to 25%.
2
Judging from the convergence in interest rates and the volume of capital flows, the integration of
global capital markets is reaching a high level of maturity, particularly in the European Union. Clearly,
the same cannot be said about the integration of labour markets [see, however, Sinn (2000) for a recent
reassessment in the face of eastern EU enlargement]. Still, mobility costs are falling in labour markets
as well and one might argue that a defining characteristic of a federation is free migration. This is also
true in the European Union where the Single Act has removed any legal barriers to individual mobility
across its member states.
1
standards, the European welfare state will be exposed to strong erosive forces which
threaten its very substance” because “the benefits of the social welfare state will [...]
attract migrants who are net recipients of public resources.” This line of reasoning
is formally captured in Wildasin (1991) who demonstrates that taxes directed at redistributing income from wealthy to poor households will be inadequately low in a common
labour market. The logic is similar to that of tax competition for a mobile tax base: if
those who benefit from redistribution are mobile, welfare migration leads to a ‘race to
the bottom’ in the choice of social benefits.3 Likewise, migration-induced inefficiencies
emerge if local public expenditures are financed with revenues from a publicly-owned
fixed factor as individuals move in seeking a share of the local rents.4
In the light of the above arguments, economic integration may seem less desirable
than a simple consideration of the potential efficiency gains from common markets would
suggest. The fundamental concern is the consequences of increased integration for redistributive policies and the resulting levels of inequality in our society. This paper
provides a new perspective on the redistributive consequences of economic integration.
We consider two jurisdictions (countries) that pursue redistributive policies at the local level. Heterogeneous individuals derive income from their given labour and capital
endowments. Factor prices are endogenous and adjust to equilibrate domestic supply
and demand of each factor. The countries redistribute income via a lump-sum transfer
to resident-workers, financed by a source-based linear tax on capital. This policy is
democratically chosen by majority vote of its inhabitants. Integration of factor markets
is modelled as the removal of all explicit or implicit barriers to mobility.5 With common
3
Similar implications of labour mobility for the scope for redistribution within the EU are discussed
in, e.g., Cremer and Pestieau (1996). That jurisdictions may be forced to lower taxes in order to avoid
attracting low-income households and repelling high-income households has already been conjectured
by Oates (1972). Brueckner (2000) provides a survey of the theoretical and empirical literature on
welfare migration. A different view of mobility is taken by, e.g., Myers (1990) and Wellisch (2000). In
line with Tiebout (1956)’s conjecture that ‘voting with one’s feet’ invokes desirable competition among
jurisdictions, these authors show that population migration may enhance the efficiency properties of
equilibria. See the discussion in Section 3.
4
See Flatters, Henderson and Mieszkowski (1974) and Boadway and Flatters (1982).
5
In particular, the integration of labour markets requires each country to treat foreign individuals
equally, i.e. immigrants cannot be subjected to discrimination on the basis of origin. In the European
Union, for example, the equal-treatment principle is guaranteed by the Treaty of Rome.
2
factor markets, changes in the policy of one country have an impact on the other other
country, because factors migrate to seek the highest income, net of taxes and transfers.
In this framework, we first study, in turn, the partial integration of capital markets
and labour markets, respectively. The analysis is taken as a benchmark to compare
against the case of full integration where both capital and labour are mobile. Relative
to a situation of non-integration (autarky), redistributive taxes are reduced under capital
market integration because countries seek to attract foreign capital, which adds to the
domestic tax base and increases wages at home. Expressed differently, because the
voters in each country ignore the effect of changes in their tax rate on the tax base of
the other country, a coordinated increase in capital taxes would be strictly beneficial
for a majority in each country. A similar result holds if we consider the integration of
labour markets in isolation. Raising taxes increases social benefits and, hence, triggers
immigration. In their attempt to reduce the number of foreign workers and beneficiaries
of their national redistributive policy, countries set taxes relatively low. Again, this
argument can be expressed in terms of an externality if one recognizes that policyinduced immigration benefits the voters abroad [see Wildasin (1991)]. Moreover, we
show that further integration of labour markets, measured as a reduction in individual
mobility cost, exasperates the problem of fiscal competition.
Having identified these two fiscal competition effects that arise from the integration
of factor markets, we then ask in a second step whether the conclusions under partial
integration carry over to the case of full integration. Our main result is that the two
effects need not reinforce but instead may neutralize each other. That is, the composite effect may well be that the problem of fiscal competition is alleviated. Specifically,
if countries are symmetric we demonstrate that further integration of labour markets
always leads to an increase in equilibrium tax rates if capital markets are already integrated. As a consequence, there is more redistribution in equilibrium and a majority of
the population in each country is strictly better off.
Although the finding may seem surprising at first glance, it has an intuitive explanation. The integration of labour markets reduces the incentives for voters to attract
foreign capital through lowering national tax rates because it at the same time causes
3
an inflow of labour, which is detrimental to a majority. In other words, the perceived
benefits from tax competition are reduced as it triggers detrimental immigration, precisely because additional capital raises both wage rates and per-capita social transfers.
Moreover, the effect is strengthened the lower the migration costs, i.e., the more pronounced the integration of the labour market. Hence, ongoing integration need not
heighten capital tax competition, provided it goes hand in hand with enhanced labour
mobility. Conversely, the result also implies that fiscal competition in the presence of
mobile individuals (labour) may be dampened as capital markets are integrated. By the
same token as above, raising social benefits (taxes) now causes a capital outflow and no
longer triggers undesirable immigration, thereby diminishing the incentives to repel the
beneficiaries of taxation through cutting down on welfare programs.6
This reasoning is quite general when countries face identical conditions. We also
demonstrate, however, that it cannot always be applied to asymmetric countries for
reasons that will become clear below.7 Intuitively, although tax competition is mitigated
as a result of full integration, high mobility of capital and labour also forces countries to
converge, both economically and politically. Therefore, countries that had an advantage
under partial integration may lose if they remove existing barriers to the mobility of other
factors as well. In other words, if countries are asymmetric, the efficiency gains and the
gains from reduced inequality resulting from full integration come at a cost: economic
and political conditions converge and so do the countries’ shares of the economy wide
surplus.
Beyond the seminal tax competition literature mentioned above, the present work
is related to several contributions to the literature on fiscal federalism. Persson and
Tabellini (1992) investigate the consequences of increasing capital market integration
and interjurisdictional competition in the context of a representative democracy. Higher
capital mobility is shown to influence the political choice of voters, which partially off6
The concern that integration intensifies tax competition is prevalent, for example, in the policy
coordination guidelines on capital tax competition recently issued by the OECD and the EU [see
OECD (1998) and EU (1998)].
7
One difficulty that arises is that countries may want to strategically manipulate their factor incomes
in addition to the pure fiscal competition effect. The former incentive is not necessarily reduced by
ongoing integration.
4
sets the effects of intensified fiscal competition. Bolton and Roland (1997) analyze the
politico-economic conditions that cause nations to split up into separate countries. The
authors note that separation cannot always be prevented by granting fiscal autonomy
because of tax competition effects. Perroni and Scharf (2001) examine how competition
for mobile capital affects jurisdiction formation. In their model, jurisdictions form endogenously and there exist scale economies in the provision of local public goods. Fiscal
competition results in an enlargement of jurisdictional boundaries and can therefore be
welfare improving. Finally, Huizinga and Nielsen (1998) consider a fiscal competition
framework where labour and capital are locally taxed. The authors demonstrate that cooperatively choosing one of the tax rates can increase the incentives for non-cooperative
tax competition on the other factor, which in turn may lower welfare. Hence, partial
(piecemeal) policy coordination may be worse than no coordination at all.8
The remainder of the paper is organized as follows. Section 2 presents the basic
model and provides an analysis of fiscal competition under the partial integration of
capital and labour markets, respectively. Section 3 considers full integration. A final
section discusses our results and concludes.
2. THE MODEL
The basic framework we use in our analysis allows both capital and labour to be
internationally mobile. As a first step, however, we will only consider partial integration (either capital or labour mobility) in Subsections 2.2 and 2.3. These settings
serve to illustrate the arguments of the existing literature on tax competition and interjurisdictional spillovers and formalize them in our model where majority voting determines policy outcomes. Subsequently, we consider full integration in Section 3 and show
in which sense those arguments must be qualified.
2.1. The basic framework
8
Fuest (1998) arrives at a similar conclusion in a different framework. Note that the focus here is on
the benefits of cooperative (or centralized) policy determination, not on the benefits of full integration
in a non-cooperative setting as in the present paper. Still, the results share the general insight that fiscal
competition may be softened by policies that are undesirable if viewed in isolation (non-cooperation
and increased integration, respectively).
5
Consider an economy that consists of two countries or regions j = 1, 2, inhabited by
a continuum of heterogeneous individuals i with mass normalized to one. Individuals
derive income from their factor endowments: each individual supplies inelastically one
unit of labour and k i units of capital. They are free to choose their residence and where
to invest their capital. Thus, both labour and capital are internationally mobile. In
what follows, we will assume that capital is perfectly mobile, i.e. there are no costs of
investing abroad. Labour, in contrast, may be less mobile than capital internationally.
This idea is captured by assuming that individuals have to incur a cost mi ≥ 0 when
they emigrate from their home country, which is derived from the following spatial
representation of the economy: suppose individuals reside on the closed interval [0, 1]
with i representing their initial location. The border is located at i = n̄1 = 1 − n̄2
so that all individuals of type i ∈ [0, n̄1 ] initially live in country 1 whereas individuals
with i ∈ (n̄1 , 1] are nationals of country 2. The individual cost of migration mi can be
expressed as a function of one’s distance to the border |i − n̄1 |, which we take to be
linear for simplicity. Hence, mi = θ(n̄1 − i) for i ≤ n̄1 and mi = θ(i − n̄1 ) otherwise
where θ ≥ 0 measures the cost of mobility.9
By definition, n̄j is the initial size of the labour force in country j. It is also equal to
its initial share of the total population. We denote country j’s initial capital stock by
K j . In addition to capital and labour, we allow for a third factor of production which is
immobile. For ease of exposition, we will refer to this factor as land although one may
also think of it as any other fixed factor such as natural resources, entrepreneurial input,
non-transferable know-how, or infrastructure. Country j is endowed with Lj units of
this factor which we assume to be publicly owned.10
9
As will become clear below, agents’ residential decisions are independent of their investment decisions. Our analysis therefore allows for any correlation between initial locations i and capital endowments k i . Also note that the migration costs can equivalently be interpreted as representing an
‘attachment to home’ (individuals have locational preferences for their home country because of cultural differences) by assuming that individual utility is given by consumption ci , plus a non-pecuniary
element mi [see, e.g., Burbidge and Myers (1994)].
10
Since we later analyze labour and capital mobility, it is necessary to include a third immobile factor
to avoid unrealistic ‘buy-out’ results as discussed in Kuhn and Wooton (1987) and to preserve some
locational fixity which is central to the definition of a jurisdiction. By assuming that the factor is owned
or controlled by the national government we are also able to study migration in an environment where
6
Labour, land, and capital are used as inputs in production by competitive firms
to produce a composite consumption commodity c. The technology F (·) is identical
across countries, i.e., any technological differences can be attributed to differences in the
countries’ initial endowments of the productive factors. If Kj , nj , and Lj are aggregate
inputs in country j, aggregate output is given by Yj = F (Kj , nj , Lj ).
Assumption 1. The production function F (·) is strictly increasing, concave, exhibits
constant returns to scale, and satisfies (subscripts denote derivatives)
a) limK→0 FK (·) = limn→0 Fn (·) = ∞
b) FKn , FKL ≥ 0.
Assumption 1. a) ensures that firms employ all inputs in positive quantities, even if
some factors are mobile and the difference in productivity across borders is relatively
large. Assumption 1. b) states that additional capital (weakly) increases the marginal
productivity of other factors of production. In what follows, it will often be convenient
to state the relevant variables in per-capita terms. Thus, let kj = Kj /nj , lj = Lj /nj
and yj = F (Kj /nj , Lj /nj , 1) ≡ f (kj , lj ) be the per-capita values that correspond to Kj ,
Lj and Yj , respectively. We denote by wj the wage rate, by rj the return to capital,
and by πj the return to the fixed factor in country j. The first-order conditions of profit
maximization imply that each factor is paid its marginal product and that profits are
zero,
rj = FK (Kj , nj , Lj ),
Yj = rj Kj + wj nj + πj Lj
wj = Fn (Kj , nj , Lj )
⇔
and πj = FL (Kj , nj , Lj ),
yj = wj + rj kj + πj lj
(1)
(2)
Countries pursue purely redistributive policies (tj , gj ) that consist of a) a source based
tax tj ≥ 0 on each unit of capital employed in country j and b) a uniform per-capita grant
the rent-sharing problem under labour mobility discussed in the Introduction is operative. Alternatively,
we could assume that the fixed factor is distributed unequally among the population and that it can be
taxed. The political process would then imply that the income accruing to owners of the fixed factor
is taxed away in full for redistributive purposes. Obviously, the outcome is therefore identical to a
situation where this factor is under public ownership.
7
gj ≥ 0 that redistributes public revenues (including those derived from the fixed factor)
among the residents of country j.11 Note that because individuals do not differ in their
labour endowments, an additional tax on labour cannot serve redistributive purposes
and can therefore be disregarded. The tax rate tj is chosen by majority vote of the
inhabitants of country j. The public budget constraint in country j is gj nj = tj Kj +πj Lj ,
or, expressed in per–capita terms,
gj = tj kj + πj lj ,
j = 1, 2.
(3)
The consumption (net income) ci of an individual with a capital endowment of k i who
lives and has invested in country j is
cij = wj + gj + (rj − tj )k i
= yj − (rj − tj )(kj − k i ),
(4)
(5)
where the last equality follows by substituting for gj from (3) and using the expression
for yj in (2). Individuals choose where to invest their capital and where to live so as to
maximize utility, taking prices and policies in each country as given.12 The government
collects the tax revenue and distributes social benefits to the residents according to the
budget (3) which endogenously determines gj once capital and labour have migrated.
Given (t1 , t2 ), the underlying model is therefore a simple general equilibrium economy
augmented by a public sector. In equilibrium, consumers maximize (5), firms maximize
profits and behave according to (1), the public budget (3) holds and prices adjust so as
to clear markets. To see how the model works across countries for, e.g., capital consider
the following. The firms’ demand for capital depends on factor prices which leads to
aggregate factor demand Kj (·) according to (1). The supply price (net return) of capital
which an investor in j faces is rj −tj ≡ ρj . Because capital is fully mobile, however, its net
return will be equalized across countries in any equilibrium, i.e., r1 − t1 = r2 − t2 = ρ.13
11
Requiring tj and gj to be non-negative ensures that the effect of factor movements on the utility of
individuals can be signed unambiguously, which simplifies the exposition and the analysis considerably.
12
Agents take the behaviour of other agents as parametric when deciding where to invest and where
to live. Because they are infinitesimally small, their individual decisions have no impact on factor prices
and public budgets and they must take these as fixed.
13
Otherwise, all investors are better off investing in the country with the higher net return, which
would be inconsistent with an equilibrium as capital demand is positive due to Assumption 1 a).
8
For ρ > 0, aggregate (and average) capital supply to the economy is k̄ = K 1 + K 2 .
Hence, market clearing requires K1 (·) + K2 (·) ≤ k̄ with strict equality if ρ > 0.
The sequence of events is as follows. First, the inhabitants in each country j simultaneously vote on the tax rate tj , taking the tax rate in the other country as given. The
second stage is the general equilibrium economy described above, which voters take into
account in their policy choice. That is, they foresee how changes in the national tax rate
tj affect factor prices and public budgets through migration and investment decisions.
An equilibrium must satisfy the following conditions: a) the implemented tax policy
is preferred to any other feasible tax policy by a majority in each country (political
equilibrium), given the foreign tax rate, and b) for (t1 , t2 ), the underlying economy is in
equilibrium.
Before closing this section it is useful to establish the existence and the general
properties of a political equilibrium. Note first that due to r1 − t1 = r2 − t2 , the
preferences of a voter in country j over tj are unaffected by her decision where to invest
her capital [see (4)]. Since we allow for positive cost of migration θ > 0, however, this
argument does not apply to voters’ residential choices. In order to ensure that a political
equilibrium exists, it is therefore necessary to assume that they disregard their own
residential choice when going to the ballot (although they still take aggregate migration
into account). This assumption on voter myopia eliminates the possibility of preference
reversals that may occur when an individual anticipates her decision to emigrate, thereby
prompting her to vote strategically in favour of the foreign country.14 Once a voter i in
country j does not take a (potential) change of residence into account, her preferences
over tj are thus given by (4), irrespective of her investment and migration decision.
Then, we see from (5) that voters’ preferences differ only through their individual capital
endowments k i . It is now straightforward to show that a majority rule outcome exists
even though preferences may not be single peaked (see the Appendix). Furthermore,
the political equilibrium in country j is the tax rate t∗j that is most preferred by the
individual with median capital endowment, kjm . Recall that k̄ is the average (and
14
See the remark for voter myopia in Section 2.3. for a discussion. It also provides an alternative
assumption that is consistent with rational expectations and could be invoked to avoid this problem.
9
aggregate) capital stock in the economy as a whole. We assume in the remainder that
the (initial) distribution of capital is skewed in the sense that the average capital stock
in the economy as a whole exceeds the median individual’s endowment in each country:
Assumption 2. kjm < k̄,
j = 1, 2,
Now suppose that Assumption 2 also holds in each country separately, i.e., kjm < k̄j ,
which is well in line with empirical observations. Given that capital owners need not
invest their capital anywhere if the returns are negative (free disposal), it follows that
under autarky where neither factor is mobile, capital income is taxed away in full: using
(5), the solution to
m
t∗j = arg max cm
j = yj − (rj − tj )(k̄j − kj )
tj
is t∗j = rj . Because yj and rj are fixed and evaluated at k̄j and ¯lj under autarky, tj is
a non-distortionary (lump-sum) tax on capital that will be imposed to the maximum
extent by a decisive majority endowed with less than the average capital stock. Although this outcome of expropriative capital taxation may be unrealistic, it implies full
redistribution and complete equality within a country (though there may still be severe
inequality across countries) and thus serves as a useful reference point against which the
effects of capital and labour mobility as successive steps of integration can be judged.15
2.2. Tax competition for mobile capital
Suppose first that individuals can freely and costlessly invest their capital in either
country but there are prohibitively high individual costs of migration. For θ → ∞,
labour is completely immobile and thus nj = n̄j , j = 1, 2. From the previous section, if
capital is perfectly mobile we must have
r1 − t1 = r2 − t2 = ρ
ρ ≥ 0,
(IE)
in equilibrium (recall that ρ denotes the common after tax return to capital). Together
with K1 + K2 = k̄, the investment equilibrium condition (IE) defines country j’s equi15
One way to restore realism would be to introduce cost of raising public funds [see, e.g., Perotti
(1993)] which, however, would complicate the analysis without providing any further insights.
10
librium capital stock Kj as a function of the policy variables t1 and t2 .16 Using rj = FKj
from (1), we can implicitly differentiate (IE) to obtain the investment responses for
ρ > 0,
1
∂Kj
< 0.
= 1
2
∂tj
FKK + FKK
(6)
Accordingly,
j
∂rj
FKK
σj ≡
= 1
∈ (0, 1) and
2
∂tj
FKK + FKK
σj − 1 =
∂ρ
∈ (−1, 0).
∂tj
(7)
If capital is mobile, raising tj lowers its net return ρ by less than under autarky where
the corresponding change would be −1. Yet, because each country has some market
power, its capital supply does not react fully elastic to changes in tj so that ∂ρ/∂tj < 0.
Using (IE), the net income (consumption) of a voter i in country j is given by (5),
irrespective of her investment decision. From the previous section, we know that the
equilibrium policy in country j is equal to the preferred policy of the individual with
median capital endowment in j, i.e., it maximizes her net income subject to (IE), and
K1 + K2 = k̄. The effect of a change in tj on the utility of the decisive voter with capital
endowment kjm in country j is
∂cm
∂rj
1 ∂Kj
j
= kj − kjm + tj
−
(kj − kjm ).
∂tj
nj ∂tj
∂tj
(8)
The first term in (8) represents the direct ‘redistributive’ effect of capital taxation: if
the median capital endowment kjm in country j falls short of its equilibrium per-capita
capital stock kj , the decisive voter is a net recipient of public transfers and this effect
is positive for a majority of the population. In contrast, if kjm exceeds kj , she is a net
contributor to the redistributive system in j and the effect is negative for a majority.
The second term in (8) is the indirect revenue or ‘tax competition’ effect: lowering
taxes is attractive because of the resulting capital inflow and the corresponding increase
in per-capita public expenditures. Finally, the last term captures the composite effect
on factor prices and, hence, on an individual’s gross income and the component of gj
16
See the Appendix for a formal argument why there can be no equilibrium where K1 + K2 < k̄.
11
financed by revenues from the publicly owned fixed factor. An increase in the tax rate
decreases wages and land rents and increases the gross return to capital because less
capital is domestically employed. This ‘factor price effect’ is negative (positive) for the
decisive voter if her individual capital endowment falls short of (exceeds) the average
capital stock invested in j.
Employing (8) and (7), the first-order conditions of the corresponding program that
characterize an interior solution can be written as
(1 − σj )(kj − kjm ) + tj ηkj = 0,
where ηkj ≡
∂kj
∂tj
=
1 ∂Kj
nj ∂tj
j = 1, 2,
(9)
is the change in country j’s per-capita capital stock as a
response to a change in its domestic capital-tax rate. Equation (9) defines tj as the best
response of the electorate in country j to the policy th chosen by the other country. The
equilibrium tax rates t∗1 and t∗2 can be found at a point where the two reaction functions
intersect.
Proposition 1. Consider an equilibrium with ρ∗ > 0 and t∗j > 0, j ∈ {1, 2}. In any
such equilibrium, a majority of the population in each country would strictly benefit if
both countries cooperatively chose to increase their tax rates.
Proof. Let cij (t∗1 , t∗2 ) be the equilibrium net income (utility) of a voter in j with a
capital endowment of k i and consider a change in both tax rates from t∗j to t̃∗j = t∗j + dt,
dt > 0. Since both countries change their tax rate by the same amount, investment
decisions are unchanged [see (IE)] and so are factor prices. The corresponding change
in a voter’s utility is
dcij = cij (t∗1 , t∗2 ) − cij (t̃∗1 , t̃∗2 ) = (kj − k i )dt,
after substituting for cij from (5). Hence, dcij > 0 ⇔ (kj − k i )dt > 0. In any equilibrium
with ρ∗ > 0 and t∗j > 0, the equilibrium policies have to satisfy (9). Because the last
term in this equation is strictly negative for t∗j > 0, we must have kj∗ > kjm . Hence,
kj∗ > k i for all individuals with less capital endowment than the median voter and
∆cij > 0 for a majority in j. ||
12
The proposition illustrates that competition for internationally mobile capital often
leads countries to implement tax rates that are ‘too low’ relative to the cooperatively
chosen levels. As a result, there is too little redistribution from the perspective of a
majority in each country. Intuitively, each country has an incentive to lower taxes
below the cooperative level because doing so causes a capital inflow which increases
per-capita transfers and wages. Expressed differently, fiscal policy in the presence of
a mobile tax base has two beneficial external effects on the foreign country. Raising
taxes at home causes an outflow of capital which a) increases foreign revenues [the fiscal
externality identified in Wildasin (1989)] and b) lowers the price of capital and increases
wages and the returns to the fixed factor abroad. From (5),
∂cih
1 ∂Kh ∂rh
∂kh
=
th
−
(kh − k i ) = th
+ (1 − σj )(kh − k i ).
∂tj
nh ∂tj
∂tj
∂tj
Clearly, this externality is positive for a majority of the population abroad if t∗h > 0 ⇔
kh > khm in equilibrium.17 This line of reasoning also explains why the above result
only holds for t∗j > 0. To see why tax rates need not always be below the cooperative
solution, suppose kh < khm ⇒ t∗h = 0 for one country h. Again, it is easy to show that
there exist changes in tax rates (dt1 , dt2 ) which make a majority in each country better
off. Yet, this will require dtj < 0, i.e. the other country’s tax rate may be ‘too high’.
The reason is that the above mentioned externality is negative: the external effect on
factor prices caused by the inflow of capital is negative for the (necessarily capital rich)
majority in h (if we allow for th < 0, the inflow of capital is also detrimental to the fiscal
budget).
Due to Assumption 2, this possibility only arises if the equilibrium is asymmetric. It is
therefore sensible to use a situation where countries are identical ex ante as a further
17
In the case where ρ∗ = 0, it is obvious that the taxation is already optimal from the view of
a (capital poor) majority as any further increase in tj would only lead to productive capital being
withdrawn from the market (see also the Appendix). Straightforward conditions under which a unique
equilibrium satisfying ρ∗ > 0 and t∗j > 0, j = {1, 2} exists are derived in Kessler et. al (2001).
13
point of reference. In a symmetric equilibrium,18 we can use σj =
1
k̄ − k m = −t∗ ηk ,
2
1
2
to obtain from (9),
ηk = (FKK )−1 < 0,
where t∗ > 0 is the commonly chosen tax rate and k m is the median capital endowment
in each country. Hence, as long as there is an economy-wide desire for a majority to
redistribute (k̄ > kjm ), we have t∗ > 0 and there will be scope for a cooperative increase
in tax rates as shown in Proposition 1.
2.3. Fiscal Competition in a common labour market
As a second prelude to our main objective of analyzing full integration of capital
and labour markets, we next consider a situation where labour is mobile but capital
is immobile. Although we do not believe this scenario to be descriptively accurate
from an empirical point of view, it allows us to illustrate the arguments of inadequate
redistribution in the presence of migration which have been put forward in the literature.
Thus, suppose capital owners are not allowed to invest their capital abroad (e.g.
there are restrictions on foreign investment) so that the capital stock in country j is
fixed and equal to its initial aggregate stock K j . Individuals can, however, decide to
change their residence and move abroad in the migration stage, taking factor prices
and policies as given. To derive the corresponding equilibrium condition, note first
that an individual’s migration decision is independent of her capital endowment k i . It
only depends on her mobility cost and the difference in wages and social benefits across
borders. Because the costs of moving are monotonic, a migration equilibrium can be
characterized by a marginal individual i∗ who is indifferent between residing in either
country. Then, all individuals with i ≤ i∗ prefer to live in country 1 while individuals
i > i∗ will live in country 2. The population sizes in both countries are
Z i∗
Z 1
∗
di = i and n2 =
di = 1 − i∗ ,
n1 =
i∗
0
18
As long as tax rates are strategic complements (the respective reaction functions are upward sloped)
asymmetric equilibria cannot exist if countries are identical.
14
i.e., country 1’s labour force n1 also denotes the marginal individual in a migration
equilibrium. We can therefore write the migration equilibrium condition as19
w1 + g1 = w2 + g2 − θ(n̄1 − n1 ).
(ME)
Together with (3) and n1 + n2 = 1, (ME) implicitly defines country j’s labour force
(population size) as a function of t1 and t2 . Let xj = wj + gj be the part of an agent’s
consumption that is not individual specific and note that
xjn ≡
1
1
∂xj
j
j
j
= Fnn
− (tj kj + FLj lj ) + FLn
lj = −( gj + FKn
kj ) < 0.
∂nj
nj
nj
(10)
The last inequality of (10) follows from substituting back for gj and the fact that factor
prices adjust to maintain zero profits. As one would expect, an inflow of additional
resident-workers reduces wages and the amount of the transfer that is available to the
population of country j. Implicitly differentiating (ME) yields
∂nj
kj
=− 1
> 0.
∂tj
xn + x2n − θ
(11)
An increase in a country’s taxation of capital raises social benefits and, hence, triggers
immigration which the voters will have to take into account when voting over tax policies.
Under our assumption that voters are myopic with respect to their own residential
decision, the preferred tax rate t∗j of the median voter in j maximizes (5) subject to
(ME). Individual consumption cm
j varies with tj according to
∂cm
j
=
∂tj
=
∂nj
∂nj
j
kj − kjm + xjn
+ FKn
kjm
∂tj
∂tj
1 ∂nj
∂rj
kj − kjm − gj
−
(kj − kjm ),
nj ∂tj
∂tj
(12)
19
To see why we can subsume migration flows in both directions by one equilibrium condition, note
that if w1 + g1 < w2 + g2 initially, people will migrate from country 1 to country 2. The condition for
the marginal individual i∗ = n1 < n̄1 to be indifferent is (ME) where the right-hand side represents her
migration cost θ(n̄1 − i∗ ). Conversely, if w1 + g1 > w2 + g2 initially, there is migration from country 2 to
country 1 and the marginal individual i∗ = n1 > n̄1 incurs θ(i∗ − n̄1 ). The corresponding equilibrium
condition then reads w1 + g1 − θ(i∗ − n̄1 ) = w2 + g2 which is again equivalent to (ME).
15
j
after substituting for the expression of xjn and using ∂rj /∂tj = FKn
(∂nj /∂tj ). Similar
to the case where capital was mobile, we can decompose the change in cm
j resulting from
a marginal increase in the domestic tax rate into a direct redistributive effect [the first
term in (12)] and an indirect effect that is due to policy-induced migration. The latter
is captured by the last two terms: an additional immigrant (worker) reduces per capita
revenues (social benefits) by
1
g
nj j
and the marginal productivity of labour (wage). Due
to FKn ≥ 0, this fall in wages is not offset by the rise in the prices of other factors
for a voter with below average capital endowment, i.e., the factor price effect is again
non-positive if kj > kjm .20
Setting (12) equal to zero gives us the condition for an interior solution for the
equilibrium tax rate, which defines the reaction functions
(1 − σj )(kj − kjm ) −
1
gj η j = 0
nj n
j = 1, 2,
(13)
where, as before, σj ≡ ∂rj /∂tj ∈ (0, 1) and ηnj ≡ ∂nj /∂tj denotes the change in country
j’s population as a response to a change in its tax rate.
Proposition 2. Consider an equilibrium with t∗j > 0 and ρ∗j > 0. In any such
equilibrium, a coordinated increase in national tax rates would increase the welfare of a
majority of the voting population in both countries.
Proof. The proof is similar to that of Proposition 1. Consider a coordinated change
in tax rates with dt1 = (k2∗ /k1∗ )dt2 > 0 such that t̃∗j = t∗j + dtj is the new equilibrium
tax rate in j. Since both countries raise their tax rate in inverse proportion to their
equilibrium capital-labour ratios, we have d(g1∗ − g2∗ ) = k1∗ dt1 − k2∗ dt2 = 0, i.e., the
difference in social benefits remains unaffected. As a consequence, residential decisions
and factor prices are unchanged in the new equilibrium [see (ME)]. The change in the
utility of a voter in j at date 0 is thus
∆cij = cij (t∗1 , t∗2 ) − cij (t̃∗1 , t̃∗2 ) = (kj∗ − k i )dtj ,
20
Recall Assumption 1. b). Requiring FKn ≥ 0 also ensures that the symmetric migration equilibrium
we study below is stable [the denominator in (11) is always negative].
16
after substituting for ci from (5). To show that ∆cij > 0 for a majority of voters in
j if t∗j > 0 and ρ∗j > 0, one can use the same argument as in the proof of Proposition 1. ||
Again, taxes are inadequately low from the perspective of a majority in each country
as long as t∗j > 0 ⇒ kj∗ − kjm > 0 and ρ∗j > 0 for j = 1, 2 in equilibrium. Each country
has an incentive to lower taxes below the cooperative level because doing so causes
some recipients of social benefits to leave, thereby increasing per-capita transfers and
wages for the remaining population. From a different perspective, this phenomenon can
be explained with positive spillovers from an increase in domestic public expenditures
(taxation): the associated inflow of immigrants at home leads to higher wages and higher
redistributive transfers [the fiscal externality in Wildasin (1991)] abroad, which benefits
the majority of the population in the foreign country.
Similar to the capital tax competition case, however, the result requires t∗j > 0 in
equilibrium. Thus, there may in general exist asymmetric equilibria where taxation
in one country is above the cooperative level.21 Let us therefore briefly characterize
a symmetric situation with ex ante identical countries. In a symmetric equilibrium,
migration is zero. Imposing symmetry on the reaction functions (13) and substituting
for the expressions of ηnj using (11) yields
k̄ − k m = k̄
g∗
,
2g ∗ + 12 FKn k̄ + 12 θ
(14)
where g ∗ > 0 is the common public transfer. Now assume that labour markets become
increasingly integrated, represented by a fall in the cost of migration from θ to θ0 , say.
Consider a symmetric equilibrium in tax policies as characterized by (14). By inspection,
the left-hand side remains unchanged when considering a new (symmetric) equilibrium
at θ0 . Since the right hand side decreases in θ and increases in g ∗ , a drop in the cost
of migration must be accompanied by a drop in the level of public services, holding all
other variables constant at their symmetric equilibrium values. Hence, θ0 < θ implies
g ∗ (θ0 ) < g ∗ (θ) and consequently t∗ (θ0 ) < t∗ (θ).
21
This can best be seen in the case where countries can impose negative transfers (head taxes) gj < 0
which we have ruled out by assumption. In such a situation, it may be preferable to attract – rather
than to deter – immigrants.
17
Corollary. Consider any symmetric equilibrium with ρ∗ > 0 and suppose that labour
becomes more mobile (increasing integration of labour markets). Then, there exists a
new symmetric equilibrium in which the common tax rate on capital is lower than in the
initial situation, i.e.,
θ0 < θ
t∗ (θ0 ) < t∗ (θ).
⇒
As a consequence, a majority of the population in each country is strictly worse off.
As labour becomes more mobile, countries perceive a higher elasticity of immigrants
with respect to a change in their level of social benefits (their tax rate). Since immigration is undesirable for a majority of the residents, this effect renders high taxes
less attractive.22 From Proposition 2, the accompanied change in the voter’s utility is
negative for a majority because a further reduction in social benefits is harmful if those
already are at inadequately low levels. We can thus conclude that increasing labour
market integration is undesirable from the perspective of the majority of the voting
population in each country, at least if countries are symmetric.
A Remark on Voter Myopia
The preceding analysis has presumed that individuals vote myopically with respect to
their own migration decision even though they correctly foresee aggregate equilibrium
migration. As mentioned above, this restriction on voter rationality rules out preference
reversals which may arise if individuals know that they will migrate to the foreign
country given the domestic policy under consideration at the voting stage, and thus
prefer policies that are beneficial from the perspective of their future country of residence
(rather than their home country). A similar assumption is implicit in some Tiebout
models on inter-jurisdictional competition [see, e.g., Epple and Romer (1991)] which
employ a general equilibrium approach where individuals move and vote simultaneously.
In this formulation voters do not take the migration decisions of their fellow citizens as
given (although they are made simultaneously to their own) and voting takes place in the
country of (future) residence, which is somewhat difficult to reconcile with any timing
of actions. While it is readily verified that both formulations yield qualitatively similar
22
An analogous argument for mobile capital can be found in Wilson (1987) and Wildasin (1988).
18
results, neither is fully satisfactory which illustrates the conceptual problems associated
with settings where residential and political decisions are intertwined.
One possibility to eliminate those difficulties in our model would be to consider voting
under the veil of ignorance. More specifically, suppose individuals when casting their
vote know their home country and their own capital endowment but not their future
type i which determines the cost of migration. An individual with home country j only
knows that i is uniformly distributed over the interval [0, n̄1 ] or [n̄1 , 1], respectively.
Using the equilibrium migration condition (ME), one can easily show that the expected
consumption of a voter in country j from a policy tj , holding th fixed, is
θ
E[ci |t1 , t2 ] = cij + Ij (n̄j − nj )2
2
where cij and nj are evaluated at (t1 , t2 ) and Ij is an indicator function which is equal to
one if n̄j > nj and zero otherwise.23 Under the veil of ignorance, voters rationally maximize expected consumption in their home country, adjusted for the additional benefit
they derive from emigration.24 Therefore, an (additional) positive bias toward emigration emerges, preserving the monotonicity properties of preferences and leaving our
results qualitatively unaffected.25
3. FISCAL COMPETITION AND FULL INTEGRATION
The previous analysis demonstrated that partial integration (of either capital or labour
markets) is detrimental to fiscal policies directed at redistributing income from the
wealthy to the poor. At first glance, one may therefore be tempted to conclude that
23
From (ME), xj = xk − θ(n̄j − nj ). Adding ρj k i on both sides yields cij = cih − θ(n̄j − nj ) (note that
it does not matter where the individual has invested her capital). The expected consumption of an
individual with home country 1, for example, is then E[ci |t1 , t2 ] = P rob{i ≤ n1 }ci1 (t1 , t2 ) + P rob{i >
n1 }[ci2 (t1 , t2 ) − Ei>n1 θ(n̄1 − i)] = ci1 + I1 θ2 (n̄1 − n1 )2 after substituting for ci2 and computing expected
migration cost.
24
Because people leave their home country only if it is beneficial to do so, their utility abroad will
exceed their utility at home with the difference being determined by the number of people who emigrated
in equilibrium [see (ME)]. As a consequence, if an individual has been assigned very low migration
costs (and thus emigrates), her expected gain over consumption at home is larger, the smaller nj .
25
Clearly, the conclusions under both alternatives are identical for θ → 0 or if one confines attention
to symmetric equilibria. Moreover, the fiscal competition argument under labour mobility (which then
translates into lower incentives to compete for mobile capital as we will show below) would be reinforced.
19
full integration of labour and capital markets intensifies fiscal competition. As will
become clear shortly, however, this presumption is misleading. Specifically, this section
demonstrates that there are plausible circumstances in which increasing labour market
integration alleviates capital tax competition (and vice versa). We consider a situation
in which individuals can both choose where to invest their capital, and where to live.
Optimal investment and residential decisions now require
r1 − t1 = r2 − t2 = ρ,
ρ≥0
(IE)
w1 + g1 = w2 + g2 − θ(n̄1 − n1 ).
(ME)
Together with (3), K1 +K2 = k̄ and n1 +n2 = 1, these two conditions define a country j’s
capital stock Kj and population size (labour force) nj as a function of t1 and t2 . Using
the implicit function theorem one can deduce the investment and migration responses
to a change in tj for ρ > 0,
and
∂Kj
h
= [g1 /n1 + g2 /n2 + FKn
(kh − kj ) + θ]/D
∂tj
j 6= h,
j, h ∈ {1, 2}
(15)
∂nj
h
= [tj /nj + th /nh − FKK
(kh − kj )]/D,
∂tj
j 6= h,
j, h ∈ {1, 2}
(16)
2
1
2
1
2
1
)(x1n +x2n −θ) < 0
+FKK
k2 )−(FKK
k1 +t2 /n2 −FKK
)(t1 /n1 −FKK
+FKn
where D ≡ (FKn
provided the equilibrium characterized by (IE) and (ME) is stable.26
As before, the equilibrium tax policy t∗j maximizes the utility (5) of the individual
with median capital endowment kjm , subject to (IE) and (ME). The change in the
decisive voter’s net consumption can be written as
∂cm
1 ∂Kj
1 ∂nj
∂rj
j
= kj − kjm + tj
− gj
−
(kj − kjm ).
∂tj
nj ∂tj
nj ∂tj
∂tj
(17)
Again, there is a direct redistributive effect from taxation. Furthermore, because both
capital and labour are mobile, there are now two indirect revenue effects that arise
from an increase in tj . Ignoring the factor price effect σj = ∂rj /∂tj for the moment, it
26
All derivations in this section are relegated to the Appendix. Using standard fix-point arguments,
it is straightforward to show that such a stable equilibrium always exists.
20
thus appears that the fiscal competition effects identified in the previous two sections
combine so as to render taxation even more unattractive. Of course, this line of reasoning
implicitly presumes that the investment and labour force responses are similar to those
that prevail under partial integration, namely, ∂Kj /∂tj < 0 and ∂nj /∂tj > 0. A closer
look at (16), however, reveals that this need no longer be the case. In fact, if tj > 0,
j ∈ {1, 2}, then ∂nj /∂tj < 0 for kj < kh , i.e., a rise in the domestic tax rate now
leads to emigration for at least one country j. This stands in sharp contrast to our
earlier result that in a situation where capital is immobile, increases in a nation’s tax
rate triggers immigration. The puzzle can be resolved by observing that kj < kh also
implies ∂Kj /∂tj < 0 by (15). If capital is mobile, the capital outflow caused by higher
taxation (and the corresponding decrease in wages and public benefits) suffices to offset
any positive effect on the government’s budget that such a raise in the tax rate might
have. Expressed differently, precisely because the capital inflow associated with a decline
in tj negatively affects the well-being of individuals living in the foreign country, those
foreigners with relatively small mobility costs will immigrate.
Before turning to asymmetric countries below, let us first examine in more detail a
situation where countries are symmetric and set a common tax rate tj = t, j = 1, 2.
As we have seen in the previous two sections, this special case yields the most clear-cut
predictions about the effects of fiscal competition and partial integration on countries’
ability to pursue redistributive policies. Imposing symmetry on the investment and
migration responses (15) and (16), we obtain
t
∂nj
|tj =t =
≤0
KL ¯
∂tj
l)
2FKK (π¯l + 14 θ − t FFKK
(18)
g + 14 θ
∂Kj
|t =t =
< 0.
KL ¯
∂tj j
2FKK (π¯l + 14 θ − t FFKK
l)
(19)
Hence, lowering the domestic tax rate now never results in (beneficial) emigration as
would be the case if capital were immobile. Moreover, the inflow of capital per capita
that can be generated by such a policy will generally be smaller than in the case where
labour is perfectly immobile (θ → ∞). To see this, observe that
21
∂kj
∂tj
=
1 ∂Kj
[
nj ∂tj
∂n
− kj ∂tjj ]
using (19) and (18) reduces to
ηk =
∂kj
|t =t = η̂k m(θ) < 0,
∂tj j
where η̂k = (FKK )−1 is the corresponding change in a situation where labour is completely immobile (Section 2.2.), and
m(θ) =
π¯l + 41 θ
KL ¯
π¯l + 14 θ − t FFKK
l
∈ (0, 1),
for t > 0 and FKL > 0. We see that m(θ) increases in θ and approaches one as θ → ∞.
Consequently, ηkj will be lower in absolute value, the lower θ: the per-capita capital
stock reacts less elastically to a change in fiscal variables because of the associated in–
or outflow of labour. The underlying reason is the following: if t > 0 ⇔ ∂nj /∂tj < 0,
a drop in tj increases labour supply in country j which encourages investment beyond
the direct tax cut effect because the marginal product of capital increases. Hence,
aggregate capital stock responds more elastically to changes in t when labour is mobile
and FKn > 0. But if FKL > 0 ⇔ −FKK k > FKn , this effect is sufficiently small so that
less capital per worker is additionally invested.27
Setting (17) equal to zero, imposing symmetry and using our usual notation, we find
that the common tax rate t∗ > 0 in a symmetric equilibrium with ρ∗ > 0 is determined
by
1
(k̄ − k m ) + t∗ ηk − 2π¯lηn = 0.
2
Observe that for θ → ∞, we have ηn → 0, ηk → η̂k and this condition reduces to the
corresponding condition for the case where only capital is mobile. The second term
reflects the combined effect of the induced factor movements on the share of public
benefits that is financed through capital taxation, while the third term represents the
rent-seeking effect already mentioned in the previous section. As argued above, ηn < 0
27
Recall from Assumption 1 that F (·) exhibits constant returns to scale. Marginal products are
thus homogeneous of degree zero and FKK k + FKn + FKL l = 0 by Euler’s law (factor prices adjust
to maintain zero profits). The argument here can also be verified formally by differentiating (IE) and
using ∂kj /∂tj = [∂Kj /∂tj − kj (∂nj /∂tj )]/nj . In what follows, however, we also allow for FKL = 0 [see
Assumption 1. b)] in which case ηk is unaffected by labour migration.
22
so that the latter effect is now positive rather than negative. Furthermore, the revenue
effect ηk is now less pronounced than in the case where labour is not mobile. Since |ηn |
decreases and |ηk | increases in θ, holding all other variables constant at their symmetric
equilibrium values, it is straightforward to show
Proposition 3. Consider a symmetric equilibrium with ρ∗ > 0 and suppose that
labour becomes more mobile. Then, there exists a new symmetric equilibrium in which
the common tax rate on capital is higher than in the initial situation, i.e.,
θ0 < θ
⇒
t∗ (θ0 ) > t∗ (θ),
t∗ (θ0 ) ≤ ρ∗ .
As a consequence, a majority of the voting population in each country strictly benefits
from increasing integration of labour markets.
Proof. See the Appendix. ||
The intuition for this result has already been laid out in the preceding discussion: in
a symmetric equilibrium under full integration, a unilateral reduction in the domestic
tax induces (detrimental) immigration. At the same time, less capital per capita can be
attracted relative to a situation where labour is not mobile. These two effects of increasing labour market integration, represented by a fall in θ, work in the same direction:
both migration and investment responses tend to discourage tax competition. Contrary
to the finding in the preceding section, a further integration of labour markets is therefore always desirable from the perspective of the majority of the voting population in
each country, provided capital markets are already integrated.
While the result requires symmetry in the initial equilibrium, we expect a similar
line of reasoning to hold more generally as well. In particular, suppose inadequately
low taxation emerges because jurisdictions compete either a) to attract a mobile tax
base or b) to repel mobile beneficiaries of taxation. Viewed in isolation, both fiscal
competition effects obviously work in the same direction. Yet, the picture changes once
they are jointly taken into account. If a country cuts taxes to attract the tax base, it
will also attract those factors that benefit from an increase in the public budget. As
23
long as the perceived gains from the cut are thereby reduced, the incentives to engage
in wasteful fiscal competition are diminished.28 This line of reasoning is most clearly
seen for vanishing cost of migration where it holds even if countries are not identical:
Proposition 4. Suppose θ → 0. Then, there exists a unique equilibrium in tax rates
(t∗1 , t∗2 ) with the following properties. For j = 1, 2,
a) (t∗j , gj∗ ) = (t∗ , g ∗ ) > 0, where ρ∗ = t∗j − rj∗ = 0,
b) kj∗ = k̄, lj∗ = ¯l ⇒ w1∗ = w2∗ and r1∗ = r2∗ ,
¯
c) ci∗
j = f (k̄, l), ∀ i.
Thus, ρ∗ = 0 in the unique equilibrium, i.e. the returns to capital are fully redistributed
among the residents in each country. Furthermore, the equilibrium is symmetric and
there is no inequality within or across countries, irrespective of national endowments or
income distributions.
Proof. See the Appendix. ||
Although it builds on the strong assumption that both factors are fully mobile,
Proposition 4 is important in several respects. First, perfect migration allows countries
to pursue redistributive policies that are completely adequate from their (equilibrium)
point of view. Like in autarky, income from capital is entirely taxed away and redistributed among all residents in the unique equilibrium [part a)]. In comparison to
Section 2.2, we can conclude that labour mobility fully eliminates inter-jurisdictional
competition to attract mobile capital, regardless of initial differences in countries’ factor endowments or national income distributions. Moreover, the converse also holds:
inter-jurisdictional competition to repel the mobile beneficiaries of taxation (labour)
disappears once capital is fully mobile. Although we have not emphasized this point in
the previous discussion, this can easily be seen by comparing Propositions 3 and 4 to
the results in Section 2.3. where such detrimental competition emerged in a common
28
Note that this logic neither depends on the nature of the tax base nor on the identity of the net
recipients of tax revenues. See also the discussion in Section 4 below.
24
labour market without capital mobility. Second, when countries are asymmetric, there
will be more redistribution than under autarky since all differences, both within and
across countries, vanish [part c)].29 This is because factor mobility helps not only to
equalize prevailing economic disparities but also reduces the political differences among
countries, i.e., it can act as a substitute for the harmonization of national tax policies
[part b)].
This last observation holds the key to understanding the argument behind Proposition 4. In particular, one can show that in any potential asymmetric equilibrium, a
majority of voters in the low-tax country strictly prefers to replicate the fiscal policy in
the high-tax country because this a) results in an efficient international factor allocation
which maximizes per-capita output at home and abroad and b) in addition increases
their redistributive benefit from taxation.30 Hence, (IE) and (ME) jointly ensure that
only symmetric equilibria in which countries set identical tax rates and converge with
respect to their per-capita factor employment can exist.
Once this result is established, the unique equilibrium must entail full taxation. To
see this, consider again the revenue effect of raising one’s tax rate, which for (tj , gj ) ≡
(t, g) and θ → 0 becomes [see (18) and (19)]
t
∂Kj
∂nj
−g
= 0,
∂tj
∂tj
j = 1, 2.
Perfect factor mobility implies that any loss in tax revenue induced by a capital outflow is
exactly offset by a reduced cost of paying the transfer because of emigration. Conversely,
any gain in tax revenue from attracting capital is lost by having to distribute this gain
to additional residents. Intuitively, given the result that any equilibrium is symmetric
and therefore efficient with respect to the international factor allocation, economy-wide
per capita output (factor income) is maximized and remains unaffected by small factor
movements in any equilibrium. At the same time, perfectly mobile capital and labour
ensure that this output is always divided up equally within the two countries. Hence, a
marginal change in tj must leave average output both economy-wide and – through the
29
30
We are grateful to an anonymous referee for making us aware of this point.
See the proof of Proposition 4 in the Appendix.
25
induced factor reallocation – for each country unchanged. But if factors change their
location of employment so as to keep average income generated in each country constant
and equal to maximal average income, no further redistribution across countries can take
place.31 For the individual voter, therefore, only the direct redistributive effect and the
indirect factor price effect σj ∈ (0, 1) are operative and a majority in each country
prefers full taxation [see (17)].
While the idea that mobility of individuals may be beneficial stands in contrast to
the widely accepted view captured formally in Section 2.3., it has already been put
forward by some contributions on fiscal federalism. In particular, Myers (1990) and
Krelove (1992) show that welfare maximizing governments providing local public goods
voluntarily propose transfer payments to achieve efficiency in public good supply and
international factor allocation if households are perfectly mobile. The driving force in
these models is that the constraints imposed by perfect mobility completely align interests across borders if the population is homogeneous. As Bucovetsky (1995) and Wilson
(1999) correctly note, however, this result rests on the unrealistic assumption that individuals are identical in every respect. Moreover, inter-jurisdictional transfer payments
must be feasible if countries are not identical. Proposition 4, in contrast, allows both
individuals and countries to differ in their factor endowments and there is no need for
countries to influence the factor allocation through international transfers. Even more
importantly, spillover effects of a mobile population are a source of inefficiency in our
framework: additional immigrants at home cause foreign (domestic) per-capita expenditures and wages to rise (fall). As Proposition 2 and its Corollary demonstrate, fiscal
competition therefore cannot be avoided even if countries are identical and individuals are perfectly mobile. Indeed, the problem becomes more severe the more mobile the
population is. This result is only reversed in Propositions 3 and 4, which consider full integration and draw on the very fact that (im)migration has undesirable consequences.32
31
Note that the direct redistributive effect always cancels out in aggregate (average) accounts and so
do terms of trade (factor price) effects in a symmetric equilibrium.
32
It is this property of our model that, among others mentioned above, contrasts most with previous
work on the benefits of population mobility. For instance, Burbidge and Myers (1994), Wellisch (2000,
Ch. 7), and Hindricks (2001) show that mobility can help to internalize inter-jurisdictional externalities.
When those externalities are absent, however, migration in these models either has a positive (efficiency)
26
From this perspective, it is the mobility of capital which causes the spillovers associated
with migration to disappear. One can therefore not conclude from our analysis that migration is welfare (or efficiency) enhancing. Rather, we provide an intuitive explanation
for why two externality effects emerging under partial integration can offset each other
when being combined under full integration.
We close this section by noting that the result in Proposition 4 also provides a
benchmark against which the residents’ utilities in a pure tax- competition situation,
that is, without labour mobility, may be compared. More specifically, it indicates that
potential efficiency and welfare gains brought about by the international equalization of
factor returns and the desired level of redistribution also come at a cost: if both capital
and labour are perfectly mobile, convergence requires countries in equilibrium to share
the economy-wide surplus equally in per capita terms. In other words, any economic
advantage that countries might have enjoyed in a situation where labour markets were
not fully integrated is levelled out. Still, it is evident that the symmetric equilibrium
in Proposition 4 cannot be improved upon from the point of view of a majority in each
country without harming a majority in the other country.33 Clearly, this outcome is
therefore one possible outcome of a situation where the countries set their tax rates
cooperatively.
4. DISCUSSION AND CONCLUDING REMARKS
We can now turn to a more detailed discussion of our main results and their implications.
Given that capital markets are already fully integrated and fiscal competition prevails,
under which circumstances could we expect a majority in each country to favour labour
market integration? Proposition 3 tells us that full integration is often strictly beneficial
and never detrimental if countries are in a symmetric situation. This is true even though
effect or no consequences at all on the prevailing equilibrium.
33
Expressed differently, this particular international allocation of productive factors and choice of tax
policies is on the international ‘Pareto frontier’ for a majority, constructed by choosing fiscal policies
and factor allocations so as to maximize the consumption of the decisive voter in the domestic country,
holding the consumption of the decisive voter in the foreign country fixed. This is true regardless of
whether or not international transfers can be made. Also, provided (tj , gj ) are the only redistributive
instruments within a country, it is easy to see that an allocation cannot be improved upon for a majority
if and only if it cannot be improved upon for the decisive voter in each country.
27
there are no efficiency gains from common markets in this case. Full integration serves
solely to soften the countries’ incentives to engage in fiscal competition. If countries
differ in important economic or political variables, however, the consequences of further
integration are ambiguous. Although a full-fledged analysis has been beyond the scope
of this paper, it is possible to identify several forces that work in opposite directions.
On the one hand, there are now efficiency gains from a common labour market that can
be realized. On the other hand, Proposition 4 suggests that full integration also tends
to equalize economic conditions across countries.34 Therefore, countries that enjoyed
a relative advantage in the situation without population mobility will now be at a
disadvantage, ceteris paribus.
Some informal insights in this regard may be gained if we draw on existing results
from the tax competition literature. For example, it has been shown that countries with
small populations gain from capital tax competition [Bucovetsky (1991) and Wilson
(1991)]. This gain will be lost if the competition is alleviated and countries converge
through migration. Thus, ex ante differences in population size can make integration
detrimental to the smaller country.35 Clearly, a similar argument applies if countries
differ in their endowments of the fixed factor, which one can also interpret as an existing
technology gap. In such a situation, the equilibrium where only capital is mobile will
favor the resource-rich or technologically more advanced country because it can attract
more capital at a given tax rate. The liberalization of labour markets reduces the gap as
workers migrate from the poor to the wealthy country, driving down wages and welfare
benefits. Hence, even though fiscal competition may be softened, only the poor country
unambiguously benefits from full integration. In contrast, it is quite possible that a
(capital-poor) majority of the population in the rich country looses and, therefore, ob34
This tendency has been confirmed in the numerical simulations we conducted to investigate the
characteristics of asymmetric equilibria under full integration and imperfect labour mobility. The
calculations also indicate that full integration maintains its mitigating effect on fiscal competition
relative to each partial integration case, albeit less pronouned.
35
Wilson (1991) compares the outcome under tax competition to the cooperative solution that treats
countries symmetrically. Translated to our framework, the latter is the unique equilibrium that emerges
under perfect labour mobility (Proposition 4). The author shows that the smaller country may well
refuse to implement this outcome. The reason is that the cooperatively optimal symmetric allocation
is dominated by the asymmetric but suboptimal allocation under tax competition.
28
jects to such liberalization. This possibility is worth emphasizing because, in practice,
national governments have faced stiff resistance to liberalize labour movements across
the European Union, and still do in the light of the EU’s eastern enlargement. Since
full integration implies economic convergence, the observation that workers in countries with relatively high wages and generous welfare payments reject integration is not
inconsistent with our model. Rather, the creation of a common labour markets only
gains political support if the countries are sufficiently alike, either because they already
share similar economic and political conditions from the outset, or because previous
integration measures have already narrowed down prevailing national differences.
The central message, however, remains that fiscal competition among countries need
not intensify as factor markets are successively integrated. Advocates of a coordination
and harmonization of European tax rates conjectured the collapse of the welfare state
as countries strive to attract taxpayers and to deter the recipients of social benefits in
a world where both groups may be expected to be increasingly mobile within the EU.
Our unified framework has allowed us to separately consider these two fiscal competition
effects and their underlying rationale in a realistic setting. We have demonstrated that
unilateral tax cuts are advantageous for a capital-poor majority in each country because
wages and public revenues rise as additional capital is employed domestically (Section
2.2). The same is true if such tax cuts serve to prevent welfare migration because
wages and per-capita revenues decrease if additional residents enter the domestic labour
market and receive public transfers (Section 2.3). Since these two fiscal competition
effects work in the same direction when considered separately, the concern is that they
combine so as to render redistributive taxation even more unattractive. Our results in
Section 3 and the accompanying logic indicate that this fear may be unwarranted. To
the contrary, these effects may well work in opposite directions if they are effective at
the same time under full integration. If the beneficiaries of social policy become mobile
as well, wasteful competition for a mobile tax base that helps to finance the welfare state
is likely to be diminished.36 Similarly, if the tax base is mobile, competition to keep out
36
Note that we have treated the decision of where to reside and where to supply one’s labour (human
capital endowment) as inseparably connected to one another. In doing so, we have implicitly disregarded
the possibility that individuals choose to work abroad but continue to live at home (e.g., through tele-
29
those who benefit from the welfare state may be reduced. The underlying rationale is
strong and quite intuitive: unilateral tax cuts, intended to attract the tax base or to
deter those who collect welfare payments, can no longer serve both purposes at the same
time because, e.g., a desirable capital inflow now results in undesirable immigration. As
a consequence, the country’s incentives to engage in such behaviour are weakened.
For this reason, we also think that our conclusions are fairly robust to various modifications and extensions of the analysis. In particular, they should qualitatively carry
over to factors of production other than ‘capital’ and ‘labour’ among which countries
redistribute factor income. As one natural variant of model, suppose for instance that
individuals differ in their earning ability (productivity of labour) only and that countries
levy taxes on labour income for redistributive purposes. Also, assume that the decisive
voter in each country has less than average productivity so that a majority favors redistribution. Clearly, if only high-skilled individuals who are net contributors to the social
system are mobile, there would be income tax competition to attract the mobile tax
base [see Proposition 1]. That high-productivity workers who move to a country to save
on income tax are eligible for the social benefits as well is immaterial in this regard:
what matters for the question of whether such workers are worth competing for is their
net contribution to the tax base, which is positive. Likewise, if only very low-skilled
workers who are net beneficiaries of the system are mobile, social benefits would drop
as the decisive majority in each country seeks to avoid welfare migration [Proposition
2]. Now suppose both groups can migrate. Although the outcome will generally depend
on the specifics of the model under investigation (on how production and factor prices
vary with factor movements), we expect the offsetting effect identified in Propositions 3
and 4 to play a non-negligible role. If reducing the income tax rate attracts high-skilled
labour (net contributors) and this ceteris paribus benefits a majority in each country,
low-skilled labour (net beneficiaries) should be attracted as well. Thus, a unilateral
income tax cut directed at enticing the rich will cause poor individuals living abroad
commuting). If increased integration of labour markets does not go hand in hand with increasingly
mobile beneficiaries of local social policies, our results on the desirability of such measures generally
will not hold. A related disclaimer applies if migrating workers are not eligible for local public transfers
(see below).
30
to immigrate, thereby reducing the perceived gain precisely because more people on
welfare hurt the majority in each country. Hence, welfare migration of the poor can
mitigate wasteful income tax competition for the rich (and vice versa).
This argument also provides some insight as to the possible effects of relaxing the assumption of homogeneous labour in our model. Specifically, assume that workers differ
not only with respect to their capital endowment, but also in their labour productivity
(which can be either high or low, say) and consider a source tax levied on total factor
income. Continue to assume that the decisive voter favors redistribution and recall that
capital investment decisions are independent of migration decisions. A negative fiscal
competition effect then arises under the partial integration of either factor market (capital, high-skilled labour, low-skilled labour) in isolation. Whether successive integration
now intensifies or alleviates fiscal competition is ambiguous and is likely to depend on
the relative mobility of factors: consider for instance the integration of labor markets
in a world where capital is already mobile. If low-skilled labour is less mobile that
high-skilled labor, tax competition may intensify because the most responsive factors
contribute (net) to the tax base (the two fiscal competition effects for capital and highskilled labour should work in the same direction). But if further integration facilitates a
common market for low-skilled labour, the third fiscal competition effect should work in
the opposite direction. As before, this effect may generate enough political support for
a further integration of labour markets, provided the countries economic and political
conditions are sufficiently similar.
Second, we have assumed that domestic voters in j choose the capital tax rate tj ,
taking as given the foreign tax rate th . Once factors have moved internationally, national
per-capita grants (gj , gh ) are determined residually from public budgets. As first noted
by Wildasin (1988), this assumption is often not innocuous: equilibria will generally
differ if instead governments choose expenditures gj , taking as given the foreign gh ,
and then passively adjust tj to balance their budgets.37 In this alternative scenario,
37
Because the residual tax rate tj cannot take arbitrary values, though, this approach suffers from
the problem that the feasible range for gj varies with the chosen gh of the other country (admissible
strategies are interdependent). Expressed differently, for some (gh , gj ), there may be no tax vector
(tj , th ) such that both countries’ budgets balance ex post.
31
our results can be shown to hold as long as we continue to confine attention to stable
equilibria in international factor movements. Then, equilibrium transfers again are ‘too
small’ if either capital or labour is mobile. Moreover, these negative fiscal competition
effects under partial integration run against each other as mobile workers follow mobile
capital under full integration.
What is important for our results, however, is that individuals are treated equally
everywhere. That is, there is no explicit or implicit discrimination against immigrants
on the basis of origin. While the equal treatment principle naturally applies within a
country, a different picture emerges if one considers an international context. Even in the
European Union, informal barriers to free residential choice remain despite the fact that
the Union guarantees free mobility and equal treatment in the Treaty of Rome and has
since adopted a series of measures directed at promoting mobility across member states.
Thus, our non-discrimination assumption may be quite strong. Yet, the observation that
it is necessary for our argument to apply sheds light on the question of whether equal
treatment is a desirable principle. From a partial integration point of view, for instance,
one could argue that abandoning the equal-treatment doctrine serves as an instrument to
moderate fiscal competition in common labour markets. Indeed, if migrating workers are
not eligible for the local redistribute transfer payments, no fiscal competition would arise
in equilibrium when capital is immobile. Our analysis, in contrast, indicates that such
measures may well work in a quite different direction if labour and capital markets are
integrated: the discrimination against immigrants in domestic social programs reduces
the mitigating effect of labour mobility and may thus help to intensify rather than to
alleviate fiscal competition.
APPENDIX
A1. Proof of the Majority Voting Equilibrium
We show that a tax rate t∗j is preferred to all other tax rates tj under majority voting in
country j if and only if it is the most preferred tax rate of the individual with median capital
endowment kjm . The argument follows Grandmont (1978). Under our assumption that voters
are myopic with respect to their own moving decision (or, alternatively, if they vote under the
veil of ignorance), only their capital endowment k i matters for their preferred policy as can be
32
seen from (5). Using the second expression in (5), the preferences of a voter with endowment
k i in country j over tj can be written as
i
m
cij (tj ) = cm
j (tj ) + ρj (tj )(kj − kj ),
(A1)
m
where cm
j (tj ) is the utility (consumption) of the voter with the median capital endowment kj
and ρj (tj ) ≡ rj (tj ) − tj . Now let tj and t0j be two different tax rates and assume without loss of
m 0
generality that the median voter prefers tj to t0j , i.e. cm
j (tj ) ≥ cj (tj ). Using (A1), this implies
cij (tj ) − cij (t0j ) ≥ ρj (tj ) − ρj (t0j ) (kji − kjm ).
(A2)
By inspection of (A2), ρj (tj ) ≥ ρj (t0j ) implies cij (tj ) ≥ cij (t0j ) for all i such that k i ≥ kjm and
ρj (tj ) ≤ ρj (t0j ) implies cij (tj ) ≥ cij (t0j ) for all i such that k i ≤ kjm . In both cases, a majority
prefers policy tj to t0j . Observe that the converse is also true, i.e., if a majority of the population
m 0
prefers tj to t0j , then cm
j (tj ) ≥ cj (tj ). Hence, the tax rate tj is preferred to all other tax rates
0
tj under majority voting in country j if and only if it is the most preferred tax rate of the
individual with median capital endowment kjm . ||
A2. Proof that the economy’s capital stock is fully utilized in any equilibrium
To show that K1 + K2 = n1 k1 + n2 k2 = k̄ in any equilibrium, suppose by way of contradiction,
j
that t1 and t2 are such that n1 k1 + n2 k2 < k̄ ⇒ ρj (t1 , t2 ) = FK
− tj = 0 for some country
j
j
is
. Since FK
j. Changes in the domestic tax rate tj then correspond to changes in FK
homogeneous of degree zero, we can write rj = FK (Kj , Lj , nj ) = fk (kj , lj ), which implies
j
j
j
j
= dtj yields
dnj . Setting dFK
dkj − n1j lj fkl
= fkk
dFK
j dkj
fkk
dtj
1 j dnj
lj
− fkl
=1
nj
dtj
⇒
dnj
dkj
≥0 ⇒
<0
dtj
dtj
(A3)
Because ρj = 0, the consumption of a voter i in j is cij = n1j F (Kj , nj , Lj ) = f (kj , lj ) for all i.
Note that all labour is supplied in equilibrium because gj ≥ 0 and wages are positive by
Assumption 1.a).
Suppose first individuals are immobile (Section 2.2), i.e., dnj ≡ 0 so that dkj /dtj < 0
from (A3). Since lowering tj strictly increases kj and therefore cij , the population in j would
unanimously prefer a lower tax rate, a contradiction to our assumption that tj constitutes an
equilibrium.
Next, consider mobile individuals. Again, we show that dcij /dtj is strictly negative. Suppose
by way of contradiction that dcij /dtj ≥ 0. Totally differentiating the migration equilibrium
condition cij = cih − θ(n̄j − nj ) then requires
dcij
dci
dnj
= h +θ
≥ 0.
dtj
dtj
dtj
33
(A4)
dn
If capital is immobile (Section 2.3), dcih /dtj = −xh dtjj since dnh = −dnj so that the right
hand side of (A4) can only be non-negative if dni /dti ≥ 0, which in turn implies dki /dti < 0
from (A3). But then, dcih /ti < 0, a contradiction.
Finally, suppose capital is mobile as well (Section 3). From (IE), ρj = ρh = 0 so that changes
h abroad. Setting dF h = 0 and using dn = −dn ,
in tj do not affect the return to capital FK
j
h
K
we obtain
dnj
1 h dnj
dkh
h dkh
+
=0
⇒
≥0 ⇔
≥0
(A5)
fkl lh
fkk
dtj
nh
dtj
dtj
dtj
Now, as cih = f (kh , lh ) due to ρh = 0, the right hand side of (A4) becomes
fkh
dnj
dkh
1
+ ( lh flh + θ)
≥ 0.
dtj
nh
dtj
Together with (A5), we therefore must have dnj /dtj ≥ 0 and dkh /dtj ≥ 0. But (A3) then
requires dkj /dtj < 0, which again contradicts dcij /dtj ≥ 0 because cij strictly decreases in nj
and strictly increases in kj . ||
A3. Derivation of the Investment and Migration Responses (Section 3)
We already know that both factors are fully employed in any equilibrium so that dn1 = −dn2
and dK1 = −dK2 . Total differentiation of (IE) and (ME) then yields the following system of
equations:
1
2
1
2
dnj
FKn + FKn
FKK
+ FKK
1
=
dtj ,
x1n + x2n − θ
x1K + x2K
dKj
−kj
j
kj > 0. Let
where xjn is defined as in Section 2.3. and xjK ≡ ∂xj /∂Kj = n1j tj − FKK
1
2
1
2
1
2
1
2
D ≡ (FKn + FKn )(xK + xK ) − (FKK + FKK )(xn + xn − θ) be the determinant of the matrix
on the left hand side. In what follows, we confine ourselves to those equilibria described by
(IE) and (ME) that are stable and thus require D < 0. Using Cramer’s rule and substituting
the expressions for xjn and xjK yields (15) and (16).
If countries are symmetric and set identical tax rates t1 = t2 = t, we must have K1 = K2 =
1
k̄,
L1 = L2 = 21 ¯l, and n1 = n2 = 12 which also implies kj = k̄, lj = ¯l and g1 = g2 = g. As we
2
will need the migration and investment responses for t1 = t2 and symmetric per-capita factor
supplies but arbitrary country sizes in the proof of Proposition 4 later, we will derive them
using k1 = k2 = k̄ and l1 = l2 = ¯l without specifying nj . To this end, note that because F (·)
is homogeneous of degree 1, we can write n1j F (Kj , nj , Lj ) = F (kj , 1, lj ) ≡ f (kj , lj ). Hence,
j
j
FK
(·) = fkj (·), FLj (·) = flj (·) and FKK
=
profits, we also have
j
FKn
=
j
−kj FKK
−
1 j
nj fkk .
j
lj FKL
As factor prices adjust to maintain zero
j
j
= − n1j (−kj fkk
− lj fkl
)≡
1 j
nj fkn .
If all functions are evaluated at their symmetric (per-capita) equilibrium values, we have
x1K + x2K = n11n2 (t − fkk k̄) and x1n + x2n = − n11n2 (g + fkn k̄) from Section 2.3. The determinant
34
D becomes
1
1
fkn (t − fkk k̄) −
fkk (−g − fkn k̄ − n1 n2 θ)
2
(n1 n2 )
(n1 n2 )2
fkk
fkn
fkl ¯
fkk
=
(g + n1 n2 θ + t
(π¯l + n1 n2 θ − t
)=
l) < 0,
2
2
(n1 n2 )
fkk
(n1 n2 )
fkk
D=
where the last equality follows from substituting g = tk̄ + π¯l and using fkn = −fkk k̄ − fkl ¯l.
From (15) and (16),
∂nj
t/(n1 n2 )
|t =t =
≤ 0,
∂tj j
D
∂Kj
(g + (n1 n2 )θ)/(n1 n2 )
|t =t =
< 0.
∂tj j
D
Inserting the expression for D into (A6), using n1 = n2 =
2fkk and FKL = 2fkl yields (18) and (19).
1
2
(A6)
and substituting back for FKK =
∂r
Finally, we derive the factor price effect σj = ∂tjj in an equilibrium characterized by (per1 = f 2 and f 1 = f 2 in such an equilibrium,
capita) symmetry. Note first that since fkk
kn
kn
kk
∂rh
1
h ∂Kj
h ∂nj
h ∂Kj
h ∂nj
= −FKK
− KKn
=−
f
+ fkn
∂tj
∂tj
∂tj
nh kk ∂tj
∂tj
nj ∂rj
nj 1
j ∂Kj
j ∂nj
fkk
+ fkn
=−
.
=−
nh nj
∂tj
∂tj
nh ∂tj
Using ∂rj /∂tj − 1 = ∂rh /∂tj from (IE) now yields σj = nh ∈ (0, 1) and when countries are
identical in size, σj = 12 , j = 1, 2.
A4. Proof of Proposition 3
Setting (17) equal to zero gives the first-order condition
(1 − σj )(kj − kjm ) +
1 ∂Kj
1 ∂nj
tj
− gj
= 0.
nj ∂tj
nj ∂tj
When considering a symmetric equilibrium with tj = th = t∗ , we can use σj =
(19) and (18). The condition reduces to
1 ∗
1
4 θt
(k̄ − k m ) = −
,
KL
¯
2
FKK [l(π − t∗ FFKK
) + 41 θ]
1
2
= nj , kj = k̄,
(A7)
which defines the common equilibrium tax rate 0 < t∗ ≤ r∗ . Holding all variables except t∗
constant at their symmetric equilibrium values, the right-hand side (RHS) of (A7) approaches
−t/FKK for θ → ∞ and (A7) reduces to the corresponding equilibrium condition in the pure
tax competition case where labour is immobile.
35
Observe that RHS increases in both θ and t∗ . Now consider an equilibrium where (A7) is
∗ , evaluated at K ∗ = 1 k̄, L∗ = 1 ¯
∗
satisfied and ρ∗ = r∗ − t∗ > 0 with r∗ = FK
2
2 l, and n = 1/2.
Because all other variables do not vary with θ or the common tax t in a symmetric equilibrium,
we can find for any θ0 < θ a tax rate t0 > t∗ such that (A7) holds at θ0 and t0 . Therefore, if
ρ0 = r∗ − t0 ≥ 0, there exists a new equilibrium satisfying (A7) with t0 > t∗ . If ρ0 < 0, i.e.,
t0 > r∗ , let the new equilibrium tax rate be t00 = r∗ . In either case, t∗ (θ0 ) > t∗ (θ) and the fall
in θ strictly improves the welfare of a majority of the voting population in each country by
the same argument as in the proofs of Propositions 1 and 2. Finally, note that θ → 0 implies
that RHS → 0, i.e. we approach full taxation for some θ >> 0. ||
A5. Proof of Proposition 4
For the proof of this proposition, the following lemma is useful:
Lemma 1. Suppose θ = 0. Then, for j, h ∈ {1, 2}, j 6= h, we have
tj
= th
=⇒
kj = kh
and lj = lh ;
tj
< th
=⇒
kj > kh
and lj ≤ lh ,
with strict inequality if tj > 0.
Proof. Recall that fj = f (kj , lj ) is per-capita output in country j. Since f (·) is concave,
fj − fh ≥ fkj (kj − kh ) + flj (lj − lh ),
j, h = 1, 2.
For θ = 0, the migration equilibrium condition (ME) can be written as fj − fh = ρ(kj − kh ).
Inserting this equation into the inequality above, setting flj = πj and ρ = (fkj − tj ) yields
tj (kj − kh ) + πj (lj − lh ) ≤ 0, j, h = 1, 2, or, equivalently,
and
t1 (k1 − k2 ) ≤ π1 (l2 − l1 )
(A8)
t2 (k1 − k2 ) ≥ π2 (l2 − l1 ).
(A9)
Consider first t1 = t2 and suppose without loss of generality that k1 > k2 . Because fkj is
decreasing in k and increasing in l, the investment equilibrium condition (IE) then implies
l1 > l2 , which together with k1 > k2 contradicts (A8). Hence, for t1 = t2 , we must have
k1 = k2 and l1 = l2 .
Next, consider t1 < t2 and suppose k1 ≤ k2 (the case t2 < t1 is analogous). (IE) then implies
l1 < l2 . But k1 ≤ k2 and l1 < l2 contradict (A9). Thus, we must have k1 > k2 which together
with (A8) implies l1 ≤ l2 with strict inequality if t1 > 0. ||
36
Proof of Proposition 4. We proceed in two steps. First we show that for θ → 0 and
< k̄, j = 1, 2, asymmetric equilibria cannot exist.
The proof uses a revealed preference argument and is by contradiction. Thus, suppose
there exist an equilibrium with asymmetric tax rates and assume t1 < t2 without loss of
generality. If this is an equilibrium, the median-income individual in country 1 must weakly
prefer t1 to any other tax rate t01 . In particular this must be true for the equilibrium tax rate
in the foreign country, t2 . From Lemma 1, if t01 = t2 , k1 = k2 = k̄ and l1 = l2 = ¯l. Hence,
kjm
m
m
m
¯
cm
1 (t1 , t2 ) = f1 − ρ(k1 − k1 ) ≥ f − ρ̄(k̄ − k1 ) = c1 (t2 , t2 ),
(A10)
where f¯ = f (k̄, ¯l) and ρ̄ = fk (k̄, ¯l) − t2 . From (ME), f1 − ρk1 = f2 − ρk2 . Inserting this
expression into (A10) yields
f2 − ρ(k2 − k1m ) ≥ f¯ − ρ̄(k̄ − k1m )
(A11)
Multiplying (A10) by n1 and (A11) by n2 and adding up, we obtain
n1 f1 + n2 f2 − ρ(k̄ − k1m ) ≥ f¯ − ρ̄(k̄ − k1m ).
Note that f¯ ≥ n1 f1 + n2 f2 because total output is maximized for kj = k̄ and lj = ¯l, j = 1, 2.
Hence, the above inequality can be satisfied only if ρ(k̄ − k1m ) ≤ ρ̄(k̄ − k1m ). Due to k̄ > k̄1m
by assumption, this is equivalent to ρ ≤ ρ̄ or, using the expressions ρ = fk (k2 , l2 ) − t2 and
ρ̄ = fk (k̄, ¯l) − t2 , to
fk (k2 , l2 ) ≤ fk (k̄, ¯l).
(A12)
From Lemma 1, however, t1 < t2 implies k1 > k2 and l1 ≤ l2 . Hence, k2 < k̄ and l2 > ¯l, a
contradiction to (A12).
Next, we show that for kjm < k̄, j = 1, 2, there exists a unique equilibrium in which
tj = r̄ = fk (k̄, ¯l). We already know from Step 1 that any equilibrium must be symmetric in
per-capita terms. Evaluating the migration and investment response functions at θ = 0 and
the (symmetric) equilibrium values (t, g) and (k̄, ¯l) yields [see (A6)],
t
∂Kj
∂nj
−g
= 0,
∂tj
∂tj
j = 1, 2.
(A13)
Inserting (A13) into (17), using kj = k̄ and σj = nh = 1 − nj , we find
∂cm
j
|t =t = k̄ − kjm − σj (k̄ − kjm ) = nj (k̄ − kjm ) > 0,
∂tj j h
for any tj = th such that n1 k1 + n2 k2 = k̄. Hence, a majority of voters in country j would
prefer a higher tax rate than th for th < r̄ ⇔ ρ > 0. Conversely, for symmetric tax rates where
ρ = 0 and n1 k1 + n2 k2 < k̄, ∂cm
j /∂tj < 0 because all voters in j prefer a lower tax than th
(see A.2 above). It follows that the unique equilibrium is t∗j = r̄, j = 1, 2 which completes the
proof. ||
37
REFERENCES
BOADWAY, R. and F. FLATTERS (1982), “Efficiency and Equalization Payments in a
Federal System of Government”, Canadian Journal of Economics, 15, 613-33.
BOLTON, P. and G. ROLAND (1997), “The Break-Up of Nations: A Political Economy
Analysis”, Quarterly Journal of Economics, 112, 1057-1090.
BRUECKNER, J. (2000), “Welfare Reform and The Race to the Bottom: Theory and
Evidence”, Southern Economic Journal, 22, 505-525.
BUCOVETSKY, S. (1991), “Asymmetric Tax Competition”, Journal of Urban Economics, 30, 167-181.
BUCOVETSKY, S. (1995) “Rent Seeking and Tax Competition”, Journal of Public Economics, 58, 337-63.
BURBIDGE, J.B. and G. M. MYERS (1994), “Population Mobility and Capital Tax
Competition”, Regional Science and Urban Economics, 24, 441-459.
CREMER, H. and P. PEESTIEU (1996), “Distributive Implications of European Integration”, European Economic Review, 40, 747-757.
EDWARDS, J. and M. KEEN (1996), “Tax Competition and Leviathan”, European
Economic Review, 40, 113-134.
EPPLE, D. and T. ROMER (1991), “Mobility and Redistribution”, Journal of Political
Economy, 99, 828-58.
EUROPEAN COMMISSION (1998), Conclusions of the ECOFIN Council Meeting on 1
December 1997 concerning taxation policy (Brussels: The European Commission).
FLATTERS, F., V. HENDERSON, and P. MIESZKOWSKI (1974), “Public
Goods,
Efficiency and Regional Fiscal Equalization”, Journal of Public Economics, 3, 99-112.
FUEST, C. (1995), “Interjurisdictional Competition and Public Expenditure: Is TaxCoordination Counterproductive?”, Finanzarchiv, 52, 478-496.
GORDON, R. H. (1983), “An Optimal Taxation Approach to Fiscal Federalism”, Quarterly Journal of Economics, 98, 567-586.
GRANDMONT, J.-M. (1978), “Intermediate Preferences and the Majority Rule”,
Econometrica, 46, 317-330.
HINDRIKS, J. (2001), “Mobility and Redistributive Politics”, Journal of Public Economic Theory, 3, 95-120.
38
HUIZINGA, H. and S. B. NIELSEN (1998), “Does Partial Tax Coordination Make
Sense?” (Mimeo, Economic Policy Research Unit, Copenhagen).
KUHN, P. and I. WOOTON (1987), “International Factor Movements in the Presence
of a Fixed Factor”, Journal of International Economics, 23, 123-140.
KESSLER, A. S., C. LÜLFESMANN, and G. M. MYERS (2001), “Economic
versus
Political Symmetry and the Welfare Concern with Market Integration and Tax
Competition”, Journal of Public Economics (forthcoming).
KRELOVE, R. (1992), “Efficient Tax Exporting”, Canadian Journal of Economics, 25,
145-55.
MYERS, G. M (1990), “Optimality, Free Mobility, and the Regional Authority in a Federation,” Journal of Public Economics, 43, 107-121.
OATES, W. E. (1972), Fiscal Federalism (New York: Harcourt Brace Jovanovich).
OECD (1998), Harmful Tax Competition: An Emerging Global Issue (Paris: Organization for Economic Cooperation and Development).
PEROTTI, R. (1993), “Political Equilibrium, Income Distribution, and Growth”, Review of Economic Studies, 60, 755-776.
PERRONI, C. and K. SCHARF (2001), “Tiebout with Politics: Capital Tax Competition and Constitutional Choices”, Review of Economic Studies, 68, 133-154.
PERSSON, T. and G. TABELLINI (1992), ”The Politics of 1992: Fiscal Policy and European Integration”, Review of Economic Studies, 59, 689-701.
SINN, H.-W. (2000), “EU Enlargement and the Future of the Welfare State – Stevenson
Lecture”, Scottish Journal of Political Economy (forthcoming).
TIEBOUT, C. (1956), “A Pure Theory of Local Expenditures”, Journal of Political
Economy, 64, 416-24.
WELLISCH, D. (2000), Theory of Public Finance in a Federal State (Cambridge: Cambridge University Press).
WILDASIN, D. (1988), “Nash Equilibria in Models of Fiscal Competition”, Journal of
Public Economics, 35, 229-240.
WILDASIN, D. (1989) “Interjurisdictional Capital Mobility: Fiscal Externality and a
Corrective Subsidy”, Journal of Urban Economics, 25, 193-212.
39
WILDASIN, D. (1991), “Income Redistribution in a Common Labor Market”, American
Economic Review, 81, 757-774.
WILSON, J.D. (1987), “Trade, Capital Mobility, and Tax Competition”, Journal of Political Economy, 95, 835-856.
WILSON, J.D. (1991), “Tax Competition with Interregional Differences in Factor Endowments”, Regional Science and Urban Economics, 21, 423-451.
WILSON, J.D. (1999), “Theories of Tax Competition”, National Tax Journal, 52, 269304.
ZODROW, G.R. and P. MIESZKOWSKI (1986), “Pigou, Tiebout, Property Taxation,
and the Underprovision of Local Public Goods”, Journal of Urban Economics, 19, 356370.
40